灰度图像的卷积很简单。您有一个形状为 nxnx1 的过滤器，并对输入图像进行卷积以提取您想要的任何特征。
我也了解卷积对 RGB 图像的作用。过滤器的形状为nxnx3。但是，过滤器中的所有 3 个“层”是否都包含相同的内核？例如，如果第 0 层是如下所示的地图，那么第 1 层和第 2 层是否也包含精确值？我问的是卷积神经网络，而不是传统的图像处理。我知道每个过滤器的权重都是学习的并且最初是随机的，我认为每一层都有不同的随机值是否正确？
【问题讨论】：
标签： conv-neural-network convolution
简短的回答是否定的。更长的答案是，每层没有一个内核，而是只有一个内核可以同时处理所有输入和输出层。
下面的代码一步一步地展示了如何手动计算每个卷积，从中我们可以看到，在高层次上，计算是这样的：
使用与核矩阵的矩阵乘法一次处理所有颜色。如果我们考虑核矩阵，我们可以看到核矩阵中用于生成第一个过滤器的值在第一列，而生成第二个过滤器的值在第二列。因此，确实，这些值是不同的并且没有被重复使用，但它们没有单独存储或应用。
import tensorflow as tf
import numpy as np
# Define a 3x3 kernel that after convolution will create an image with 2 filters (channels)
conv_layer = tf.keras.layers.Conv2D(filters=2, kernel_size=3)
# Lets create a random input image
starting_image = np.array( np.random.rand(1,4,4,3), dtype=np.float32)
# and process it
result = conv_layer(starting_image)
weight, bias = conv_layer.get_weights()
print('size of weight', weight.shape)
print('size of bias', bias.shape)
重量大小（3、3、3、2）
偏差大小 (2,)
# The output of the convolution of the 4x4x3 image input
# is a 2x2x2 output (because we don't have padding)
result.numpy()
数组([[[[-0.34940776, -0.6426925],
[-0.81834394，-0.16166998]]，
[[-0.37515935，-0.28143463]，
[-0.60084903, -0.5310158 ]]]], dtype=float32)
# Now let's see how we can recreate this using the weights
# The way convolution is done is to extract a patch
# the size of the kernel (3x3 in this case)
# We will use the first patch, the first three rows and columns and all the colors
patch = starting_image[0,:3,:3,:]
print('patch.shape' , patch.shape)
# Then we flatten the patch
flat_patch = np.reshape( patch, [1,-1] )
print('New shape is', flat_patch.shape)
patch.shape (3, 3, 3)
新形状是 (1, 27)
# next we take the weight and reshape it to be [-1,filters]
flat_weight = np.reshape( weight, [-1,2] )
print('flat_weight shape is ',flat_weight.shape)
flat_weight 形状为 (27, 2)
# we have the patch of shape [1,27] and the weight of [27,2]
# doing a matric multiplication of the two shapes [1,27]*[27,2] = a shape of [1,2]
# which is the output we want, 2 filter outputs for this patch
output_for_patch = np.matmul(flat_patch,flat_weight)
# but we haven't added the bias yet, so lets do that
output_for_patch = output_for_patch + bias
# Finally, we can see that our manual calculation matches
# what Conv2D does exactly for the first patch
output_for_patch
数组([[-0.34940773, -0.64269245]], dtype=float32)
如果我们将其与上面的全卷积进行比较，我们可以看到这正是第一个补丁
数组([[[[-0.34940776, -0.6426925],
[-0.81834394，-0.16166998]]，
[[-0.37515935，-0.28143463]，
[-0.60084903, -0.5310158 ]]]], dtype=float32)
我们会为每个补丁重复这个过程。如果我们想进一步优化这段代码，而不是一次只传递一个图像补丁 [1,27]，我们可以一次传递 [batch_number,27] 个补丁，内核将同时处理它们并返回 [batch_number, filter_size]。
【讨论】：